Distribution law

Example of the distribution law

The law of meanness is the law of distribution, but it does not yet have a mathematical model, but many other laws have a fairly clear mathematical description, for example, the normal distribution law or the Poisson distribution. Distribution, distribution function, distribution law - it's all the same, mathematical description of the probability of an event. For example, on the way to work, you sometimes go to the store to buy water, for you it's just a store, and the shopkeeper already has the law of distribution and the shopkeeper knows when you will come in and how much water to buy for a week! Here's how he did it:

In life

In this way, information was collected about various events in all corners of the world: how many ants live in an anthill, how fast the substance burns, the average earnings in the country, and so on. Then we began to notice that different events (an event is a fact of interest to us) have the same graphs of the distribution law, for example, considering the operation of the telephone exchange during the year, it turned out that the law of distribution of calls per minute has the following form:

Here, for example, the probability that 4 people will call within a minute is 17.55%, the probability that 2 people will call is 8.42%, the probability that 5 people or less will call is 61.6%.

Hypothesizing

And now, having a probability distribution, we can make various assumptions, for example, in the case of a telephone exchange, we can to put forward the assumption that in order to serve 87% of calls, we need to answer 7 calls per minute (the probability that 7 people or less will call is 86.6%, we rounded up). In order to serve 93% of calls, we need to answer 8 calls per minute and so on.

The shopkeeper may assume that if he buys 4 bottles of water a week, the probability that there will be no water when you need it is 16.6%, in turn, the probability that he will not sell all the water - 56.7%.

The law of distribution of a discrete quantity

The considered examples have a discrete form, i.e. the event X has certain values. It happens that a discrete distribution is not suitable, that it is necessary to talk about ranges of values, for example, if you measure the amount of water in a glass: You are not measuring the number of atoms, and the volume, while there is always an error, if you measured 99.92 ml, then it can be 99.925, or 99.922365, or 99.25552323 and so on, so so, in order not to include all these values in the table, you include only the rounded value and in the end you get a table, graph or function again:

How to make a distribution law

Now you know that in order to make a distribution law, it is necessary to collect data and arrange them in the form of a graph (or table, if we are talking we are talking about discrete quantities). The compilation of the distribution law is the result of the collection of statistical data, then this law is used for decision-making.

• Collect data
• Present data in numerical form
• Organize data

Distribution laws used

At the moment, there are a huge number of distribution laws, without a doubt, the Gauss distribution (normal distribution) is the most popular, because it describes any "normal" event, also, in production and the service sector is often used Poisson distribution, for example, in queue theory or as in the example about a telephone exchange.